Mass spectrometer - no deflection

[jsmith613]

Homework Statement

In one type of mass spectrometer the ions are passed through a velocity selector. This is a pair of parallel plates 2.5 cm apart. A pd of 140 V is applied to create an electric field. A magnetic field is also applied so as to give a force in the direction opposite to the field.
Calculate the magnetic field strenght needed to allow uni-positive (loss of 1 electron) neon-20 ions (mass = 3.32 * 10^-26) to pass un-deflected through a velcoity selector
The neon-20 ions are moving at 3 * 10⁵ ms^-1

Homework Equations

The Attempt at a Solution

So I think the way to do this is to equate
BqV = mv²/r

so B = mv²/rqV
B = 10671.428... T
(using a radius of 2.5/200)

The answer given is 1.8 * 10^-2 T
How??

 

[technician]

In a velocity selector there are 2 field... a magnetic field and an electric field between the parallel plates.
The moving ion experiences a force due to the magnetic field and a force due to the electric field.
What can you say about these forces if the ions are undeflected?
Do you know how to calculate both forces?

 

[jsmith613]

In a velocity selector there are 2 field... a magnetic field and an electric field between the parallel plates.
The moving ion experiences a force due to the magnetic field and a force due to the electric field.
What can you say about these forces if the ions are undeflected?
Do you know how to calculate both forces?

as the forces are ppd, I would say they would be deflected
the only way there would be no deflection is if they acted along the same line but in opposite directions.

anyway
magnetic force = BqV
E = Force/Q

I presume your saying they are equal but surely it would still be deflected :S

 

[technician]

The fields are at right angles to each other...they are called 'crossed fields'
You are correct to see that if there is no deflection then the 2 forces must be equal so...
Bqv = Eq ...this means that v = E/B
Can you find E and knowing v...get the answer

 

[jsmith613]

The fields are at right angles to each other...they are called 'crossed fields'
You are correct to see that if there is no deflection then the 2 forces must be equal so...
Bqv = Eq ...this means that v = E/B
Can you find E and knowing v...get the answer

yes
E = V/d
Eq where q = 1.6 * 10^-19
q and V are known so we can find B

but how to cross fields produce no resultant force?

 

[technician]

E = V/d = 140/0.025
The force due to the electric field is in the opposite direction to the force due to the magnetic field. When these forces are equal there is no overall force and the ion beam is undeflected.
you need to remembeer that the magnetic force is at right angles to the velocity of the ions

 

[jsmith613]

E = V/d = 140/0.025
The force due to the electric field is in the opposite direction to the force due to the magnetic field. When these forces are equal there is no overall force and the ion beam is undeflected.
you need to remembeer that the magnetic force is at right angles to the velocity of the ions

ok so what would a diagram of velocity, electric force and magnetic force look like
this would prob clear it up for me :)

 

[technician]

first of all... did you get B = 0.018T?
These 3 quantities are vectors at right angles to each other so if you draw v along the x-axis and E along the y-axis then B is along the z axis

 

[jsmith613]

first of all... did you get B = 0.018T?
These 3 quantities are vectors at right angles to each other so if you draw v along the x-axis and E along the y-axis then B is along the z axis

well I got 0.018666667 as the speed I gave was actually an approx (I worked out the actual speed in a previous part of the question)

but if B and E are ppd to each other then the forces won't cancel, will they?

so the electric force is in the same plane and same direction as E (up)

as neon are +ive, we have (by flemming left)
second finger to the right
mag field into page and force upward
so we have two upward forces?

 

[technician]

I got 0.0187T...that is the answer...just rounding off...not very important.
Using your notation...+ ions moving to right, so second finger to right.
B into paper so force due to magnetic field is up.
This means that the + plate must be at the top and the - plate at the bottom to give the electric force down

 

[jsmith613]

I got 0.0187T...that is the answer...just rounding off...not very important.
Using your notation...+ ions moving to right, so second finger to right.
B into paper so force due to magnetic field is up.
This means that the + plate must be at the top and the - plate at the bottom to give the electric force down

oh because it is not deflected, by definition the +ive plate MUST be at the top as the particle, due to e-field would move down?

 

[technician]

That's it...you have got it

 

[jsmith613]

That's it...you have got it

thanks, although this is what the textbook ms says:

magnetic field perpendicularly out of page if top plate is +ive
to check, does this assume particles are moving to the RIGHT?

 

[technician]

is there a diagram in the textbook?
If the field is out of the page and the +ions are moving to the LEFT then the + plate is at the top and the - plate at the bottom.

 

[jsmith613]

is there a diagram in the textbook?
If the field is out of the page and the +ions are moving to the LEFT then the + plate is at the top and the - plate at the bottom.

thanks
no diagram but I just wanted to check if I go it right :)